Importing VSE project as sequence to another project
Many questions here, and plenty of complexity. Short answer is that the Blender doesn't support a form of EDLs so taking your project to Resolve or such will be difficult.

Your frame slippages are codec related. It is possible that one of the timestamp settings may help. If all else fails, render to frames and then set your strips to the frames.

The only way to conform shots is to dump them down to singular channels and render our reels of your cuts with black "slugs" to hold frame counts. If you collapse your final edit down to one or two tracks, they will hold sync because of the black slugs.